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High School Mathematics
13.8 Transformations Review - II

A transformation is an operation that moves or changes a geometric figure in some way to produce a new figure. The new figure is called the image. Another name for the original figure is preimage.

A transformation can be shown using an arrow.

Three main types of transformations:

  • Translation moves every point of a figure the same distance in the same direction.

  • Reflection uses a line of reflection to create a mirror image of the original figure.
  • Rotation turns a figure about a fixed point, called the center of rotation . Rays drawn from the center of rotation to a point and its image form the angle of rotation.
Translations, reflections and rotations are three types of congruence transformations. A congruence transformation changes the position of the figure without changing its shape and size.
Another name for congruence transformation is isometry. An isometry is a transformation that preserves length and angle measure.


  • A dilation is a transformation that stretches or shrinks a figure to create a similar figure.
  • It is a type of similarity transformation.
  • In a dilation, a figure is enlarged or reduced with respect to a fixed point called the center of dilation.
  • The scale factor of the dilation is the ratio of a side length of the image to the corresponding side length of the original figure.

Directions: Choose the correct answer. Also draw 5 examples for each type of transformation: reflection, translation, rotation and dilation.
Q 1: Identify the transformation:


Q 2: Image of (3,2) under translation defined by
(x,y) (3x, 2y).

Q 3: Identify the transformation:


Q 4: Identify the transformation:


Q 5: Identify the transformation:


Q 6: Identify the type of transformation:


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Question 8: This question is available to subscribers only!

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